[Q1~12]Aclothingstoreisconsideringtwomethodstoreducetheselosses:1)tohireasecurityguardvs.2)toinstallcameras.Aftercollectingdatafor5-monthperiodeachrespectively,themonthlylosses(in100)wererecordedinthetable.Themanagerwouldinstallthecamerasonlyiftherewasenoughevidencethattheguardwasbetter. ̅ s2 n Guard (x1) 27 20 32 23 38 Cameras (x2) 48 31 29 38 44 ) 2 a) Compute the average, variance in the above table. (Show ( − ̅ calculation!) b) Test whether you use equal variance or not. (b-1) Setup hypotheses. (b-2) F-stat = (b-3) Fcrit region: (b-4) Conclusion: Assumetheequal-variancet-statisticfortheabovetwopopulations c) T-test about μ1 – μ2. (c-1) Setup hypotheses. Conclusion must include - Whether you can reject H0 or not - Explain in the problem context. (c-2) Compute SD & d.f. d.f. = 1 1 1 2 + ? ( ) �� SD= ? ?𝑛 𝑛 (c-3) t-stat = � = � (c-4) rejection region: (c-5) Conclusion: Becausehiringtheguardismoreexpensive,themanagerrequiresthatthereducinglosses(in100)whenhiringtheguardmustbeatleast2 d) 2nd t-test (d-1) Setup hypotheses. H1 ) �� (d-2) t-stat = � = � (d-3) Conclusion: Since t-stat 1 2 (BA 2606 MID-2) 2 [Q13~19]Hopingtoimprovesales,onecompanydecidedtointroducemoreattractivepackaging.Totesttheeffectonsales,themanagerdistributesthenewdesigntoSupermarket1(MKT1),whilesendingtheolddesigntoSupermarket2(MKT2).Thebarcodedatawerereceivedafteracertainperiod.Thecodeforthisproductwas9077inbothsupermarkets.Sincethecostfornewpackageismoreexpensive,themanagerwantstoknowtheeffectivenessofthisnewdesign.Thecollecteddataforthetotaltransactions(n)andthenumberof9077(x)isasfollows: a) Set up the alternative hypothesis. b) Fill up the table. (Use 3 decimal point calculation.) What is the pooled proportion for (p1 – p2)? 1 1 + ? c) Compute the standard error for (p1 – p2). ? ?𝑛 𝑛 d) What distribution does (p1 – p2) follow? MKT1 MKT2 Total n 904 1038 x 180 155 p ) Why not t-distribution? . 𝒑 −𝒑 ? 𝟏 𝟏 e) Compute z-statistic: ( ? 𝑺𝑫 f) What is zcrit at α = 0.05? Explain where you get the number. P(Z g) Conclusion: Since Becausethenewdesignismoreexpensive,themanagementrequiresthenewdesignoutsellstheoldonebyatleast2%.Inthisassumption,pleaseanswerforthefollowingquestions. ? ? 1 1 𝑛 ? h) Compute the standard error for (p1 – p2). ? ?𝑝(1−𝑝) 1 ? ? ) � − 𝑝 𝟏 𝟏 2 𝑺𝑫 i) Compute z-statistic: ( �−𝒑 ( 1−𝑝) Speeds(km/h) 20 30 40 50 60 ABS(x1) 36 48 60 67 70 non-ABS(x2) 34 51 64 69 73 d = x1 – x2 [Q22~27]TofindtheeffectivenessofABS,acarbuyerorganizedanexperiment.HehitthebrakesatsomespeedandrecordedthetimetostopanABS-equippedcarandanotheridenticalcarwithoutABS.Thespeedsandthetime(in0.1seconds)tostopondrypavementarelistedhere.CanweinferthatABSisbetter(thatis,thestoppingtimeisshorter)with95%confidence? a) What kind of comparison is this question about? b) Set up the alternative hypothesis, using d = x1 – x2. c) Compute d in the table and the average and standard deviation

1. [Q1~12]Aclothingstoreisconsideringtwomethodstoreducetheselo
sses:1)tohireasecurityguardvs.2)toinstallcameras.Aftercollecting
datafor5-
monthperiodeachrespectively,themonthlylosses(in100)wererecor
dedinthetable.Themanagerwouldinstallthecamerasonlyiftherewas
enoughevidencethattheguardwasbetter.
̅ s2 n
Guard (x1)
27
20
32
23
38
Cameras (x2)
48
31
29
38
44

2. )
2
a) Compute the average, variance in the above table. (Show ( −
̅ calculation!)
b) Test whether you use equal variance or not.
(b-1) Setup hypotheses.
(b-2) F-stat =
(b-3) Fcrit region:
(b-4) Conclusion:
Assumetheequal-variancet-statisticfortheabovetwopopulations
c) T-test about μ1 – μ2.
(c-1) Setup hypotheses.
Conclusion must include
- Whether you can reject H0 or not - Explain in the problem
context.
(c-2) Compute SD & d.f. d.f. =
1 1
1 2
+ ?

3. ( )
��
SD= ? ?� � (c-3) t-stat = � = �
(c-4) rejection region:
(c-5) Conclusion:
Becausehiringtheguardismoreexpensive,themanagerrequiresthatt
hereducinglosses(in100)whenhiringtheguardmustbeatleast2
d) 2nd t-test
(d-1) Setup hypotheses. H1
)
��
(d-2) t-stat = � = �
(d-3) Conclusion: Since t-stat
1 2
(BA 2606 MID-2) 2
[Q13~19]Hopingtoimprovesales,onecompanydecidedtointroduce
moreattractivepackaging.Totesttheeffectonsales,themanagerdistr
ibutesthenewdesigntoSupermarket1(MKT1),whilesendingtheold
designtoSupermarket2(MKT2).Thebarcodedatawerereceivedafter
acertainperiod.Thecodeforthisproductwas9077inbothsupermarke
ts.Sincethecostfornewpackageismoreexpensive,themanagerwants
toknowtheeffectivenessofthisnewdesign.Thecollecteddataforthet
otaltransactions(n)andthenumberof9077(x)isasfollows:
a) Set up the alternative hypothesis.

4. b) Fill up the table. (Use 3 decimal point calculation.) What is
the pooled proportion for (p1 – p2)?
1 1
+ ?
c) Compute the standard error for (p1 – p2). ? ?� �
d) What distribution does (p1 – p2) follow?
MKT1 MKT2 Total n 904 1038
x 180 155 p
)
Why not t-distribution? .
�
−�
?
� �
e) Compute z-statistic: ( ? ��
f) What is zcrit at α = 0.05? Explain where you get the number.
P(Z
g) Conclusion: Since
Becausethenewdesignismoreexpensive,themanagementrequiresth
enewdesignoutsellstheoldonebyatleast2%.Inthisassumption,pleas
eanswerforthefollowingquestions.
? ?
1 1
�
?
h) Compute the standard error for (p1 – p2). ? ?�(1−�) 1

5. ?
?
)
� − �
� � 2
��
i) Compute z-statistic: ( �−� ( 1−�)
Speeds(km/h)
20
30
40
50
60
ABS(x1)
36
48
60
67
70
non-ABS(x2)
34
51

6. 64
69
73
d = x1 – x2
[Q22~27]TofindtheeffectivenessofABS,acarbuyerorganizedanex
periment.Hehitthebrakesatsomespeedandrecordedthetimetostopa
nABS-
equippedcarandanotheridenticalcarwithoutABS.Thespeedsandthe
time(in0.1seconds)tostopondrypavementarelistedhere.Canweinfe
rthatABSisbetter(thatis,thestoppingtimeisshorter)with95%confid
ence?
a) What kind of comparison is this question about?
b) Set up the alternative hypothesis, using d = x1 – x2.
c) Compute d in the table and the average and standard
deviation of d. [Show your calculations!]
̅
Σ

7. n
�=�
̅
d) What distribution does �f �ollow?
−2−0
1
e) Compute t-statistic and tcrit at α = 0.05: �=� .049 =
f) Conclusion:
[Q28~34]Aprofessorisinterestedinwhetherstudentsindifferentdeg
reeprogramsearndifferentamountsintheirsummerjobs.Asampleof
4studentsintheBA,BSc,andBBAprogramswere
(BA 2606 MID-2) 3
askedtoreportwhattheyearnedtheprevioussummer.Theresults(in$
100s)arelistedhere.Canweinferthatstudentsindifferentdegreeprog
ramsdifferintheirsummerearnings?BA
BSc
BBA
37 37 39
32 49 54 42 39 59
49 47 56 Grand mean
mean mean mean

8. a) Compute the group means and the grand mean in the table.
b) Compute SST, SSE and SSTotal using the blank space in the
table.
�
?
2
SSE = ∑∑? � − ̅ =
−
?
2
SSTotal = ∑∑? � ̿ SST =
c) Fill up the following table. (Fcrit is at α = 0.05.)
Show the formula for SSTotal & SST as SSE.
Total
d) Conclusion: Since We.
[Q35~38] The employee absenteeism costs of North American
companies more than $100 billion per year. The personnel
manager recorded the weekdays during which individuals in a

9. sample of 200 absentees were away over the past several
months. Do these data suggest that absenteeism is higher on
some days of the week than on others?
Weekday Mon Tue Wed Thu Fri SUM Number of Absent (f)
49 37 35 39 40 200
Expected Absent (e) (f-e)2/e
a) What is the null hypothesis? H0:
b) What is Expected Absent (e) for Wednesday? Show your
calculation.
c) Fill up the table including (f-e)2/e.
d) What is the χ2 statistic?
e) Rejection region at α = 0.05: If χ2 > χ2 (Do not say with p-
value. Use χ2 crit.)
e) Conclusion: Since We
2
�
( ) )
(BA 2606 MID-2) 4
Year2000
Year2005
Year2010
Total

10. Firearm (1)
161
175
131
467
Knife (2)
36
37
24
97
Other (3)
53
39
27
119

11. No weapon (4)
159
166
126
451
Total
409
417
308
1134
[Q39~42]Everyyear,therearemorethan300,000robberiesintheUnit
edStates.Aresearchertookarandomsampleofrobberiesin2000,2005
,and2010,andrecordedtheweaponused:1=Firearm,2=Knifeorother
cuttinginstrument,3=Other,and4=Noweapon.Canweinferthattheu
seofweaponsinrobberiesdifferedoverthethreeyears?
a) What is the statistical independence?
1134

12. b) What is the expected frequency for type “1” weapon in Year
2005? = 417∗ 467
171.73
c) What is closest to the “(f-e)2/e” for type “1” weapon in Year
2005? = (175−171.73)2 d) What is d.f.? = (r-1)(c-1) = (3-1)(4-
1) = 6
e) What is the χ2 crit at α = 0.05? χ2 0.05,6 = 12.6
f) If χ2 statistic = 4.76, what is your conclusion?
[Q43-
50]Tohelpdeterminehowmanybeerstostocktheconcessionmanager
atYankeeStadiumwantedtoknowhowthetemperatureaffectedbeers
ales.Accordingly,shetookasampleof10gamesandrecordedthenum
berofbeerssold(in1,000bottles)andthetemperature(in°F)inthemid
dleofthegame.Weusethelinearregressionmodelofy=b0+b1x.Temp
(x)786872887284Beers(y)201114301728
( − ̅) (�−��?)� − ̅ (�−��? 2 ( − ̅)(�−��?)�
�? � 1 0 1 0 0
20.967
-9 -9 81 81 81
11.297 -5 -6 25 36 30
15.165 11 10 121 100 110
30.637 -5 -3 25 9 15
15.165 7 8 49 64 56
26.769
)
2
(�? −��? � 0.935
75.742 23.377 113.146 23.377 45.819

13. 7720 SUM302 290 292 282.396
a) Fill up the table. (From ( − ̅) to ∑( −
̅)(�−��?).�)
̅
)
)
2
b) What is ∑( − 2, ∑(�−��? �, and ∑( −
̅)(�−��?)?�302, 290 and 292
�
0 1
̅ ?
)( )
�= =
c) Compute the regression line, say �=�� + � �. (Show
your calculations with 3 decimal point.) ∑(�−���−��
̅
)
2
1 ∑(�−��
d) What is the estimated value for x = 79? �? �
���
�
∑
�−��
? ?
( )
2

14. ∑
�−�
?
( )
2
e) The SSR was partly computed in the table. What is R2? =
�=���= f) Fill out the following ANOVA table about
regression.
SourceofVariationSSdfMSFFcrit Regression (R)
Residuals (E) Total
g) What is the sb1 (the standard error for parameter b1)?
R = ,
�1�
�
�
2
∑
(
�−��
̅
)
2
crit
(FormulasforMidtermTest)
TABLES:
(BA 2606 MID-Formula)
̅
�−��
0
√
�
0
�

15. 0 0
�/�
�/�2
?
��
? ??
�
Ch 12. t- �=��/��with d.f = n – 1; z-test of p
�=�? �−�� �(But, CI = �̂±�� ��)
2
� �
� �
2
1 2
1 �
1 2
2 2
�+�
Ch 13. Equal-variance t-test of μ1 – μ2: SD = ? �? + 1 ? where
�= ��+��, with d.f = ν1 + ν2. 1 2 1 12
�
���
� +���
1 2
( )
2
2
1 2 �
1 2
2 2
� �
� 1 2
Unequal-variance t-test of μ1 – μ2: SD = √� �+ � �where
� �= �, with d.f = ���/�+���/�.

16. 1 2 1 2
2 2 2 2
1−�,� �,��, �
1 2 2 1
F-test of �/�: F = �/�� (note: ���,� = 1/�� , use α =.05/2
for equal variance test.)
?
-test of �
Ch 14. Source of variation SS d.f Treatment SST
k - 1
Error SSE n - k Total SSTotal n - 1
MS F MST MST/MSE MSE
F where
�
SSTotal = (SS from ̿), �,�−�1,�−��
SSE = (SS from ̅) and
2
SST =∑ ? ̅− ̿?
?
� ��
1
� �
�/�2,� �
Fisher’s LSD: � −�� ��? + 1 ? compared with |�−
�|�, (Bonferroni adj. used α' = α ÷ kC2) � �
?
[

17. � � � 1 2 �
]
.
Tukey’s ω: = �(�,�)���/ ��wh�ere = �/�1/ + 1/
+ ...+1/ �
2
�
−�
( )
2
�
�
�
Ch 15. Goodness-of-Fit: �= ∑�=�1 ��with d.f.=k – 1.
2
�
−�
�
?
2
�
�
�
∑
�
̅ ?
Statistical Independence Test: �= ∑ ∑ ? ���� with d.f. = (r –
1) (c – 1). ��
�
�
2
∑
(
�−��

18. ̅
)
2
1 0 1 0 1
Ch 15. Regression: �= �=� (�−��)�(�−��) and �= �?
−���̅from �=��+ � �.
2 2 2
�
) ) )
ANOVA Table: SSR = ∑(�? −��? �, SSE = ∑(�−��? �(with
d.f = n-2), SST=SSTotal = ∑(�−��? �
2 ���
���
Standard Error for b1: �= � = ? ���
? (�−�1)�
StandardNormalTableforPr(Z<z-
value)z.00.01.02.03.04.05.06.07.08.091.5 .9332 .9345
.9357 .9370 .9382 .9394 .9406 .9418 .9429
.9441 1.6 .9452 .9463 .9474 .9484 .9495 .9505
.9515 .9525 .9535 .9545 1.7 .9554 .9564 .9573
.9582 .9591 .9599 .9608 .9616 .9625 .9633 1.8
.9641 .9649 .9656 .9664 .9671 .9678 .9686
.9693 .9699 .9706 1.9 .9713 .9719 .9726 .9732
.9738 .9744 .9750 .9756 .9761 .9767 2.0 .9772
.9778 .9783 .9788 .9793 .9798 .9803 .9808
.9812 .9817 2.1 .9821 .9826 .9830 .9834 .9838
.9842 .9846 .9850 .9854 .9857 2.2 .9861 .9864
.9868 .9871 .9875 .9878 .9881 .9884 .9887
.9890 2.3 .9893 .9896 .9898 .9901 .9904 .9906
.9909 .9911 .9913 .9916 2.4 .9918 .9920 .9922
.9925 .9927 .9929 .9931 .9932 .9934 .9936 2.5

19. .9938 .9940 .9941 .9943 .9945 .9946 .9948
.9949 .9951 .9952 2.6 .9953 .9955 .9956 .9957
.9959 .9960 .9961 .9962 .9963 .9964 2.7 .9965
.9966 .9967 .9968 .9969 .9970 .9971 .9972
.9973 .9974 2.8 .9974 .9975 .9976 .9977 .9977
.9978 .9979 .9979 .9980 .9981
CriticalValueofF-dist;α=.05CriticalValueofF-dist;α=.025 ν2 ν1
1 2 3 4 5 ν2 ν1 1 2 3 4
1 161.4 199.5 215.7 224.6 230.2 1
647.8 799.5 864.2 899.6 2 18.51 19.00
19.16 19.25 19.30 2 38.5 39.0 39.2
39.2 3 10.13 9.55 9.28 9.12 9.01 3
17.4 16.0 15.4 15.1 4 7.71 6.94 6.59
6.39 6.26 4 12.2 10.6 9.98 9.60 5 6.61
5.79 5.41 5.19 5.05 5 10.0 8.43 7.76
7.39 6 5.99 5.14 4.76 4.53 4.39 6
8.81 7.26 6.60 6.23 7 5.59 4.74 4.35
4.12 3.97 7 8.07 6.54 5.89 5.52 8 5.32
4.46 4.07 3.84 3.69 8 7.57 6.06 5.42
5.05 9 5.12 4.26 3.86 3.63 3.48 9
7.21 5.71 5.08 4.72
10 4.96 4.10 3.71 3.48 3.33 10 6.94 5.46 4.83 4.47 11
4.84 3.98 3.59 3.36 3.20 11 6.72 5.26 4.63 4.28 12
4.75 3.89 3.49 3.26 3.11 12 6.55 5.10 4.47 4.12 13
4.67 3.81 3.41 3.18 3.03 13 6.41 4.97 4.35 4.00 14
4.60 3.74 3.34 3.11 2.96 14 6.30 4.86 4.24 3.89 15
4.54 3.68 3.29 3.06 2.90 15 6.20 4.77 4.15 3.80
t-Table(Criticalvalue)d.f
t0.05
t0.025
2
2.920
4.303

20. 3
2.353
3.182
4
2.132
2.776
5
2.015
2.571
6
1.943
2.447
7
1.895
2.365
8
1.860
2.306

21. 9
1.833
2.262
10
1.812
2.228
20
1.725
2.086
30
1.697
2.042
40
1.684
2.021
50
1.676
2.009

22. 60
1.671
2.000
70
1.667
1.994
∞
1.645
1.960
5 d.f χ20.05χ20.025 921.8 1 3.84 5.02
39.3 2 5.99 7.38 14.9 3 7.81 9.35 9.36 4 9.49 11.1
7.15 5 11.1 12.8 5.99 6 12.6 14.4 5.29 7 14.1 16.0
4.82 8 15.5 17.5 4.48 9 16.9 19.0 4.24 10 18.3
20.5 4.04 11 19.7 21.9 3.89 12 21.0 23.3
3.77 13 22.4 24.7 3.66 14 23.7 26.1 3.58
15 25.0 27.5